Referring to Book 2 of Elements, given a segment AB, find a point C between A and B such that the lengths of segments satisfy |AC| > |CB| as well as the following proportionality relation:
|AC| / |AB| = |BC| / |AC|

Please show me how exactly this can be translated into the quadratic equation for
x = |AC| / |AB|: x^2 + x - 1 = 0